Let us, for the sake of argument, consider six CDs, all recorded in a six-month period of 2011-2012, all featuring a tenor saxophonist. Dave Douglas’ Be Still contains jazz interpretations of traditional hymns and folksongs, and the tenor solos are straightforward, vivid and concise. On Douglas’ follow-up to Be Still, Time Travel, the edgy tenor player is a little outside the pocket. Barry Altschul’s The 3dom Factor has an exhilarating, prodigious, volatile tenor player. (Carla Bley’s “Ictus” is always fast, but not this fast.) On Slippery Rock, by Mostly Other People Do the Killing (MOPDtK), the tenor player is a performance artist, a virtuoso of musical lunacy. Unhinged, by Jon Irabagon’s Outright!, is state-of-the-art postmodern small-ensemble creative music, with compelling contributions from everyone, including the tenor player. Irabagon’s I Don’t Hear Nothin’ But the Blues, Volume 2: Appalachian Haze is a true lease-breaker. In its 48 minutes of unrelieved, outrageous uproar, the tenor player makes Albert Ayler sound like Scott Hamilton.

Actually, Irabagon is the tenor player on all six albums. His extraordinary eclecticism is meaningful only because of his exemplary execution. His saxophone sound is always clarion and clean, and his ideas are hard and clear and fresh within their respective genres. “The great thing about Jon is that when he encounters a new or unfamiliar situation he doesn’t retreat,” says trumpeter Douglas. “He plays a lot of different ways, searching for the tone that best suits that moment. And because he has such a broad vocabulary, he is able to come back to it with a new solution and a new feeling every time. Jon’s records may seem like they skitter crazily among styles and approaches. It seemed like that to me too. That’s why I hired him.”

Irabagon began to get noticed in 2008, when he won the Thelonious Monk International Jazz Saxophone Competition. He topped the “Rising Star” alto saxophone category of the 2011 DownBeat Critics Poll, and placed third on tenor saxophone in 2012. (His versatility extends to instruments. He plays four saxophones, clarinet and flute.) These days it seems like the most adventurous players in New York all want Irabagon in their bands. He keeps turning up in important projects, like guitarist Mary Halvorson’s critically acclaimed quintet (and soon-to-be septet).

Like most overnight sensations, Irabagon isn’t. He moved to New York in 2001. “It takes time to build a network in New York,” he explains, “especially with my stuff. When no one knows who you are, and you’re diverse, people just think you’re crazy. For several years, my visibility was hampered because people couldn’t figure me out. The prevailing attitude is ‘This guy does this, so if you need someone to do this, call him.’ For me it was a long, slow-building process.”

He attributes his diversity to his family background and Chicago roots: “My parents loved music. The radio was always on. Frank Sinatra. John Denver. Michael Jackson. Kenny Rogers. We didn’t think in styles or eras.” Born in 1978, he grew up in the suburbs of Chicago, got serious about the alto saxophone in high school (“Cannonball was my guy”) and gigged all through college at DePaul. “Chicago has so many kinds of music,” he says. “By the time I left, I was playing six or seven nights a week: one night a Stan Kenton cover band; the next night completely free improv; then a jazz quartet playing standards; then a disco wedding band; then a Brazilian band where everyone spoke Portuguese but me. I think the key to playing any style is to truly get inside it. You need to be around people who live and breathe it. Then you get a sense of what makes it authentic.”

Irabagon says his interest in free jazz developed early: “The improvisation scene in Chicago is strong. When I was growing up there, Ken Vandermark was proclaiming a viable, celebrated option for a kind of jazz other than playing standards in a restaurant. And the AACM heritage was still alive, with people like Matana Roberts.”

When he relocated to New York, he spent four years acquiring a master’s degree at Manhattan School of Music and an Artist Diploma at Juilliard. MOPDtK, that notorious, poll-winning troupe of merrymakers, started up in 2003. “Moppa [Elliott], Peter [Evans], Kevin [Shea] and I played non-financially-rewarding gigs in East Village basements for the first five or six years,” Irabagon recalls. “There’s a lot of responsibility for all of us, living in that freewheeling kind of moment.” The deadpan, off-the-wall wit of MOPDtK sometimes calls for Irabagon to rasp one note in perpetuity, or drill down like a jackhammer, but also allows him to soar straight up for startling, complex, passionate solos. “Music is the most serious thing in the world to me,” he says. “I spend the majority of every day working on it. But I also believe humor is a valid way of expressing things in music. I want to play with people who aren’t afraid to have fun.”

Unhinged is Irabagon’s most complete statement to date, as bandleader, composer, arranger, player and instigator of organized mayhem. (Along with Appalachian Haze, it is one of the two initial releases on his own Irabbagast label.) The concept is “songs that reference specific sub-genres in the overarching umbrella of jazz.” He warns that the shifts between genres can be “trapdoor-like.” The styles include freebop (“Camp Douglas”), Latin (“Lola Pastillas”), swing (“Parker Posey”), Paul Desmond improbably filtered through Coltrane (“Take Five”), fusion (“Kremzeek”) and Gil Evans on acid (“Silent Smile [Urban Love Song]”). Irabagon’s quintet (trumpeter Ralph Alessi/pianist Jacob Sacks/bassist John Hébert/drummer Tom Rainey) distorts these “sub-genres,” celebrates them, satirizes them and blows them up. Alessi plays with abandon yet retains his signature erudition and precision.

The killer is “Silent Smile.” After Hébert’s long, involved bass intro, a huge orchestral mass looms into view. It turns out that Irabagon had, he explains, “invited 28 friends and students into the studio and bought a bunch of beer.” “Silent Smile” gradually becomes a roiling volcanic eruption, a sublime din. “I’ll never forget the sound all those people made in the studio,” he adds. “It was one of my happiest moments in recording.”

Unhinged is a work of serious creativity and wild revelry. If you haven’t heard Jon Irabagon, it is where you should start. Just watch out for those trapdoors.